Problem: Simplify. $i ^ {6}$
The most important property of the imaginary unit $i$ is that ${i ^ 2} = {-1}$ When this property is plugged into $i ^ 4$ , we get: $i ^ 4 = ({i ^ 2}) ^ 2 = ({-1}) ^ 2 = 1$ So, we can reduce the exponent by multiples of 4 and have the same result. The remainder after dividing 6 by 4 is 2, so $i ^ {6} = i ^ {2}$ As stated above, ${i ^ 2} = {-1}$ $i ^ {6} = i ^ {2} = -1$.